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FLASH particle therapy provides a novel route for sparing healthy tissue in radiotherapy.
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The FLASH sparing effect is dependent not only on dose rate but also on linear energy transfer (LET).
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Analytical model is developed to calculate the FLASH sparing effect (FSE).
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Our model suggests that the FLASH effect is significant only when the oxygen concentration is at an intermediate level (10 ∼ 100 mmHg) and low-LET region (<100 keV/μm).
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The precise treatment planning system is required to optimize both dose rate and LET.
Abstract
Purpose
Normal tissue sparing has been shown in preclinical studies under the ultra-fast dose rate condition, so-called FLASH radiotherapy. The preclinical and clinical FLASH studies are being conducted with various radiation modalities such as photons, protons, and heavy ions. The aim of this study is to propose a model to predict the dependency of the FLASH effect on linear energy transfer (LET) by quantifying the oxygen depletion.
Methods
We develop an analytical model to examine the FLASH sparing effect by incorporating time-varying oxygen depletion equation and oxygen enhancement ratios according to LET. The variations in oxygen enhancement ratio (OER) are quantified over time with different dose rate (Gy/s) and LET (keV/μm). The FLASH sparing effect (FSE) is defined as the ratio of DFLASH/Dconv where Dconv is the reference absorbed dose delivered at the conventional dose rate, and DFLASH is the absorbed dose delivered at a high dose rate that causes the same amount of biological damage.
Results
Our model suggests that the FLASH effect is significant only when the oxygen amount is at an intermediate level (10 ∼ 100 mmHg). The FSE is increased as LET decreases, suggesting that LET less than 100 keV/μm is required to induce FLASH sparing effects in normal tissue.
Conclusions
Oxygen depletion and recovery provide a quantitative model to understand the FLASH effect. These results highlight the FLASH sparing effects in normal tissue under the conditions with the intermediate oxygen level and low-LET region.
The goal of radiation therapy is maximizing damage to the tumor while minimizing damage to the normal tissue. Dose is known as a major factor affecting tissue damage. However, it has been recently shown that not only the dose but also the dose rate is a critical factor to minimize the normal tissue damage [
]. Preclinical studies have recently discovered that dose delivered in a few milliseconds (i.e., high dose rate) have remarkable benefits in sparing healthy tissue while preserving anti-tumor activity compared to conventional radiotherapy with low dose rates [
]. Well-oxygenated cells are more sensitive to ionizing radiation due to the more free radical production, which damages DNA. It is proposed that the oxygen rediffusion can be slow under FLASH condition, based on very high dose-rate irradiation (pulse amplitude ≥ Gy/s), short beam-on times (≤100 ms) and large single doses (≥10 Gy), leading to hypoxia conditions with increased radio-resistance in normal tissue [
Particle therapy is a promising option for clinical translation of FLASH radiotherapy. For x-ray beam, the electron heat deposition on the target restricts its beam intensity, making generation of ultra-high dose rate challenging [
FLASHlab@ PITZ: New R&D platform with unique capabilities for electron FLASH and VHEE radiation therapy and radiation biology under preparation at PITZ.
]. On the other hand, carbon ion, has not only the physical but also the biological properties of densely ionizing radiation, can reach high dose rates for triggering FLASH effects and the Bragg peaks associated with heavy ions make them attractive FLASH modalities for targeting deep-seated tumors [
]. However, the oxygen effect is large only in the case of low-LET (linear energy transfer) radiations because in the dense tracks there is more direct action and less chance of indirect interactions with free radical molecules. Therefore, to successfully implement FLASH radiotherapy while securing the inherent advantages of heavy ions, the FLASH effects should precisely be quantified based on those two major physical factors: LET and the dose rate [
In this study, we propose the mathematical framework to estimate FLASH effects for heavy ion therapy based on oxygen enhancement ratio (OER) and linear energy transfer (LET). This framework has a potential to be extended for the treatment design of high LET particle therapy.
Methods and materials
Normal tissue cells undergo oxygen depletion and oxygen recovery during irradiation, as shown in Fig. 1. When the oxygen depletion rate and oxygen recovery rate differ, the environmental oxygen concentration changes, resulting in a different cell survival rate than that of pre-irradiation. Using these two different cell survival rates, the FLASH sparing effect quantifies how much radio-resistance is increased in the irradiated normal tissue cells.
Fig. 1The schematic diagram of the FLASH sparing effectiveness modeling.
We integrate the pre-existing two frameworks to evaluate oxygen enhancement under the various LET beam condition. The first model is about oxygen depletion in high-dose rate condition. The second one describes the oxygen enhancement ratio values according to LET.
The first equation is derived from an ordinary differential equation that models the oxygen recovery and depletion within normal tissue cells during irradiation by Petersson et al. [
]. A detailed derivation of this equation can be found in section 1 of the supplemental material. During the high dose rate radiotherapy delivery time, the environmental oxygen concentration of irradiated normal tissue exponentially decreases over time due to a faster oxygen depletion rate than the oxygen recovery rate.
The second equation describes radiation damage as a logistic function of oxygen concentration based on the Alper-Howard-Flanders form [
]. In order to obtain time-averaged radiosensitivity parameters such as alpha and beta during the radiotherapy duration (T), we integrated the incorporated time varying radiosensitivity parameter equations and then divided them by T. Therefore, the time-averaged radiosensitivity parameters, and , are a function of environmental oxygen concentration (Oenv) and LET. A detailed description is provided in section 2 of the supplemental material [
The FLASH sparing effect (FSE) is defined as the ratio of DFLASH/Dconv where Dconv is the reference absorbed dose delivered at the conventional dose rate, and DFLASH is the absorbed dose delivered at a high dose rate that causes the same amount of biological damage (section 3 of the supplemental material).
Results
Fig. 2 shows the variation of radiosensitivity alpha (α) depending on the oxygen concentration. Related model parameters are shown in Table 1. The FLASH sparing effect (i.e., decreased radio sensitivity) is maximized in the intermediate oxygen concentration (10–100 mmHg). However, it is not observed if the oxygen concentration in either too high (greater than10,000 mmHg) or low (less than1 mmHg) as Peterson previously reported [
]. As shown in Fig. 2, the FLASH sparing effect variations decreases as LET increases.
Fig. 2The average value of radiosensitivity α depending on the oxygen concentration for two radiation modalities of (a) low-linear energy transfer (LET) = 1 keV/µm and (b) high-LET = 100 keV/µm under the irradiation condition of various dose rates = 0.1, 1, 5, 20, 100, and 1000 Gy/s and dose = 15 Gy.
The FLASH effects are quantified by varying either oxygen concentration (Fig. 3) or radiation quality parameter, LET (Fig. 4). Fig. 3 and Table 2 represents the photon case with hypoxic tumor and aerobic normal tissue under the fixed LET = 2 keV/μm. Assuming that the ultra-high dose rate has 1000 Gy/s, the FSE values for aerobic normal tissue cells and the hypoxic tumor cells are 2.03 and 1.33, respectively (Table 2). The FLASH effect nearly doubles if the oxygen concentration is intermediate of 10–100 mmHg in normal tissue. However, the FLASH effects are insignificant if the oxygen concentration is either too high or low (Fig. 3).
Fig. 3The variation in FLASH sparing effectiveness (FSE) depending on environmental oxygen concentration (Oenv) by different dose rate at 10% cell survival when LET is 2 keV/μm.
Fig. 4The variation in FLASH sparing effectiveness (FSE) depending on linear energy transfer (LET) by different dose rate at 10% cell survival when Oenv is 20 mmHg.
As shown in Fig. 4, the increased LET minimizes the FLASH effect. When the environmental oxygen level is fixed at 20 mmHg, which is intermediate between the tumor and normal tissue, variations of the FSE along LET are demonstrated in Fig. 4. Assuming that the ultra-high dose rate has 1000 Gy/s, the FSE values for the normal tissue cells and the tumor cells are 1.87 and 1.20 respectively (Table 3). The clinically relevant carbon ion uses LET of the entrance region (normal tissue) of ∼ 20 keV/μm while the one of the Bragg peak region (tumor) of ∼ 230 keV/μm. Therefore, the FLASH effect may maintain in the normal tissue under the irradiation of entrance low-LET beam.
Table 3An eample condition with the fixed oxygen concentration of 20 mmHg for carbon ion.
]. Our study suggests that the FLASH effect is shown only in the intermediate oxygen concentration level of approximately 10 to 100 mmHg. Normal tissue with oxygen concentrations of 20–60 mmHg is the appropriate oxygen concentration for the FLASH effect. However, the FLASH effect may not be observed if the oxygen concentration is either too high or too low. Therefore, our study results recommend the preclinical investigator carefully determine the oxygen concentration in the tumor before conducting the FLASH experiment.
Our model also suggests that the FLASH effect decreases as LET increases. Since the carbon ion radiotherapy demonstrates LET approximately 230 keV/um at the Bragg peak region, where the tumor region is located, the FLASH sparing effect is not expected to be seen in the tumor cells. However, one must carefully choose the energy and path of carbon ion to avoid high-LET region in the normal tissue. Our results clearly show that, for carbon FLASH, the precise treatment planning system is required to optimize not only the dose rate but also LET.
The FLASH effect is expected to be greater at high dose rates. For low-LET, the greater oxygen depletion with a high dose rate leads to the greater tissue-sparing effect. However, our model shows that the reversed FLASH effect is expected with 500 keV/μm or higher LET beams. In other words, the anti-FLASH effect is shown at LET higher than 500 keV/μm. Further preclinical experiments are necessary to warrant the finding of the model.
Other theoretical approaches have been introduced to quantify FLASH effects in various conditions. For example, Jones uses the concept of micro-volumetric energy transfer rate (MVET) to calculate adjusted proton RBE under the FLASH dose rate condition [
]. The MVET concept assumes a ‘denser’ number of particles per unit volume resulting in more clustered DNA damage with the FLASH dose rate. However, MVET is hardly measurable thus its concept should be further validated against experimental data. Frank Van den Heuvel et al. propose an oxygen dose histogram to calculate the DNA damage in FLASH radiotherapy [
]. The oxygen dose histogram approach inheritably incorporates LET effects and comes to the same conclusions as our study (described in their supplementary material for the case of protons with different energies). We expanded the investigation into oxygen’s role in the FLASH effect to include the clinical case of carbon and α particles with LET greater than 50 keV/μm.
In a recent in vivo study conducted by Walter Tinganelli et al.[
], the ultra-high dose rate (18 Gy for 150 ms) of carbon ion induced the FLASH effects compared to the conventional dose rate (∼18 Gy/min) with 14.5 ∼ 15.5 keV/μm of LET on target. We compared our model-derived FSE with the amounts of non-damaged tissue in carbon ion experiment. The approximate FSE of the study is 2.9 using LET of 15 kev/μm, which is considerably higher than that of 1.8 derived from our FSE model using the same LET and dose rate. A detailed description is provided in Supplementary section 4.
We speculate that this difference originated from two major causes: 1) the different methods to estimate the normal tissue complication, and 2) the different experimental conditions. The aforementioned study calculated the normal tissue damage from visible structural changes in the irradiated muscle, while our study calculated the linear quadratic survival curve of the cells. Moreover, the study was conducted under in vivo experiments - a model of mouse osteosarcoma - where various factors simultaneously effects, such as intercellular interactions, which require further quantification associated with the FLASH effect to be incorporated in our FSE model.
Various FLASH mechanisms such as immune and free-radical depletion as well as oxygen effect are being proposed as the FLASH has gained great attention to the research community [
]. Our study shows that the FLASH dose modification factor (i.e. the FLASH sparing effectiveness) is estimated to be approximately double compared to conventional dose rate. However, several in vivo studies in normal tissue reports more than 80% FLASH dose modification [
]. Therefore, the systematic records of the potentially-relevant radiation parameters are necessary to reveal the FLASH mechanism further and build a reliable FLASH model. Other experimental methods, such as the use of a DNA-based phantom [
], are also required to aid in the mechanistic understanding of the FLASH. More FLASH experiments in high-LET beam are also needed to validate our model.
Conclusions
Our model proposes that the FLASH effect is the most effective at oxygen concentrations of 10 to 100 mmHg. Our result also shows that the FLASH effect greatly decreases as LET increases. Thus, the FLASH sparing effect is expected under the conditions of both the intermediate oxygen concentration and low-LET region.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported by grants from the National Research Foundation of Korea (NRF, No. RS-2022-00144273 and No. 2021R1C1C1005930) funded by the Korea government (MSIT).
Appendix A. Supplementary data
The following are the Supplementary data to this article:
FLASHlab@ PITZ: New R&D platform with unique capabilities for electron FLASH and VHEE radiation therapy and radiation biology under preparation at PITZ.
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